3x(4x+5)=7(4x+5)

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Solution for 3x(4x+5)=7(4x+5) equation: 


Simplifying
3x(4x + 5) = 7(4x + 5)

Reorder the terms:
3x(5 + 4x) = 7(4x + 5)
(5 * 3x + 4x * 3x) = 7(4x + 5)
(15x + 12x2) = 7(4x + 5)

Reorder the terms:
15x + 12x2 = 7(5 + 4x)
15x + 12x2 = (5 * 7 + 4x * 7)
15x + 12x2 = (35 + 28x)

Solving
15x + 12x2 = 35 + 28x

Solving for variable 'x'.

Reorder the terms:
-35 + 15x + -28x + 12x2 = 35 + 28x + -35 + -28x

Combine like terms: 15x + -28x = -13x
-35 + -13x + 12x2 = 35 + 28x + -35 + -28x

Reorder the terms:
-35 + -13x + 12x2 = 35 + -35 + 28x + -28x

Combine like terms: 35 + -35 = 0
-35 + -13x + 12x2 = 0 + 28x + -28x
-35 + -13x + 12x2 = 28x + -28x

Combine like terms: 28x + -28x = 0
-35 + -13x + 12x2 = 0

Factor a trinomial.
(-5 + -4x)(7 + -3x) = 0


Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4x = 0 + 5
-4x = 0 + 5

Combine like terms: 0 + 5 = 5
-4x = 5

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-1.25, 2.333333333}

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